Skip to main content
SpringerLink
Log in

A rapidly converging technique for vibration analysis of plates with a discrete mass distribution

  • Published:
Ingenieur-Archiv Aims and scope Submit manuscript

Summary

A technique based on the Galerkin approach has been developed for determination of the natural frequencies of rectangular plates with discrete masses added. The technique is applied to the rectangular plates with simply supported and clamped boundary conditions, but no difficulty exists in applying the same method to the plates of various forms with different boundary conditions. The results of this technique applied to one particular case are compared to a solution obtained by an exact method; the comparison shows the two methods to be in excellent agreement.

Übersicht

Es wird eine auf dem Galerkin-Verfahren basierende Methode zur Berechnung der Eigenfrequenzen rechteckiger Platten mit diskreten Einzel-Massen angegeben. Es werden einfach aufgelagerte und eingespannte rechteckige Platten untersucht, jedoch ergeben sich keine Schwierigkeiten bei der Anwendung derselben Methode auf Platten anderer Formen mit anderen Randbedingungen. Für einen Sonderfall werden die Ergebnisse der Berechnungen mit exakten Lösungen verglichen, wobei eine ausgezeichnete Übereinstimmung festgestellt werden kann.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. L. Amba-Rao, J. Appl. Mech. 31, Trans. ASME 86 (1964) Ser. E, p. 550.

    Google Scholar 

  2. Thein Wah, Natural Frequencies of Plate-Mass Systems, Proc. Seventh Congress Theor. Appl. Mech., Bombay, India, 1961.

  3. W. F. Stokey and C. F. Zorowski, J. Appl. Mech. 26, Trans. ASME 81 (1959) Ser. E, p. 210.

    Google Scholar 

  4. M. M. Stanišić, Quart. Appl. Math. 12 (1955) p. 361.

    Google Scholar 

  5. M. M. Stanišić and R. M. McKinley, Z. Angew. Math. Mech. 41 (1961) p. 414.

    Google Scholar 

  6. S. G. Mikhlin, Variational Methods in Mathematical Physics, Oxford-London 1964, p. 489.

  7. B. A. Finlayson and L. E. Serwin, Appl. Mech. Rev. 19 (1966) p. 735.

    Google Scholar 

  8. D. Young, J. Appl. Mech. 17, Trans. ASME 72 (1950) p. 448.

    Google Scholar 

  9. R. E. D. Bishop and D. C. Johnson, The Mechanics of Vibration, Cambridge University, 1960.

  10. D. Young and R. P. Felgar Jr., Tables of Characteristic Functions Representing Normal Modes of Vibration of a Beam. Univ. Texas Publ. No. 4913, 1949.

Download references

Author information

Author notes

  1. M. M. Stanišić

    Present address: Purdue University, 47907, Lafayette, Indiana, USA

  2. J. G. Payne

    Present address: The Aerospace Corporation, 95085, Los Angeles, California, USA

Authors and Affiliations

    Authors
    1. M. M. Stanišić
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. J. G. Payne
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Stanišić, M.M., Payne, J.G. A rapidly converging technique for vibration analysis of plates with a discrete mass distribution. Ing. arch 37, 189–195 (1968). https://doi.org/10.1007/BF00532608

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF00532608

    Keywords

    Search

    Navigation